A $1000$ gallon tank is used to make a slurry for an oil$-$drilling operation. The tank takes in water at a rate of $100$ gallons$/$minute and has a $3-$inch outlet pipe that is connected to a pump that delivers the slurry to the drill bore.

a$.$ Make a sketch of the tank, noting the given information.

b$.$ What do you define as the system and what are its boundaries for this problem? Note that on your diagram.

c$.$ What is the speed the water in the outlet pipe?

d$.$ How does this speed compare to typical "economic" pipe velocities $(6f\frac{t}{sec},$ de Nevers, $p.221).$ Do you think replacing the outlet pipe with a pipe of larger $($or smaller$)$ diameter would be a good idea? If so$,$ what do you recommend? If not, why not?